We consider a finite acyclic quiver Q and a quasi-Frobenius ring R. We then characterise Gorenstein-projective modules over the path algebra RQ in terms of the corresponding quiver representations over R, generalizing the work of X.-H. Luo and P. Zhang to the case of not necessarily finitely generated Q-modules. The proofs are based on Model Category Theory. In particular we endow the category Rep(Q, R) of quiver representations over R with a cofibrantly generated model structure, and we recover the stable category of Gorenstein-projective R-modules as the homotopy category Ho(Rep(Q,R)).

Quiver representations and Gorenstein-projective modules / Meazzini, Francesco. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 2532-3350. - ELETTRONICO. - 42:(2021), pp. 1-33.

Quiver representations and Gorenstein-projective modules

MEAZZINI, FRANCESCO
2021

Abstract

We consider a finite acyclic quiver Q and a quasi-Frobenius ring R. We then characterise Gorenstein-projective modules over the path algebra RQ in terms of the corresponding quiver representations over R, generalizing the work of X.-H. Luo and P. Zhang to the case of not necessarily finitely generated Q-modules. The proofs are based on Model Category Theory. In particular we endow the category Rep(Q, R) of quiver representations over R with a cofibrantly generated model structure, and we recover the stable category of Gorenstein-projective R-modules as the homotopy category Ho(Rep(Q,R)).
2021
Quiver representations; Gorenstein-projective modules; model categories
01 Pubblicazione su rivista::01a Articolo in rivista
Quiver representations and Gorenstein-projective modules / Meazzini, Francesco. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 2532-3350. - ELETTRONICO. - 42:(2021), pp. 1-33.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/961527
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